1. Field of the Invention
This invention relates to analogue-to-digital converters for both continuous and sampled data analogue signals, and to digital modulators, especially of the sigma-delta type.
The invention is particularly concerned with means of stabilising higher order converters and modulators, that is, with three or four, or possibly more filter stages.
1. Background Information
A fourth order sigma-delta converter/modulator is illustrated in FIG. 1. It comprises quantising means for producing a digital output, oversampled relative to the signal bandwidth, and a feedback path 2 with circuit element 2a having transfer function .beta. (.beta. is usually unity gain with phase shift/delay to produce the effect of negative feedback). The feedback path feeds the feedback signal to be combined with input V.sub.in at adder 3, so that an error signal representing the difference between the input and its representation in digital form by the quantising means 1 is fed into fourth order band pass filter means 4 of overall transfer function A. In the case of the analogue-to-digital converter for continuous analogue signals, the feedback path includes a digital-to-analogue converter so that the error signal represents the difference between the analogue input and its digital representation converted to analogue form. The output of the filter means is fed along a feedforward path to quantising means 1. The quantising means 1 is typically single bit (in the digital case, V.sub.in would be multi-bit), and the design permits improved signal to noise ratio to be obtained from coarse quantisation by shaping the quantisation noise spectrum to suppress it in a desired bandwidth (GB-A-2 232 023).
A typical quantisation noise spectrum is shown in FIG. 2. There is a notch in the quantisation noise spectrum at one quarter of the sampling frequency of the quantising means 1. The pass band of the converter/modulator is chosen to coincide with this, or other notches. The depth of the notch, and hence the signal-to-noise ratio, increases as the number of filter stages increases.
Unfortunately the tendency of the converter/modulator towards instability also rises as the number of filter stages increases. For example, consider the analogue-to-digital case in which the feedback path includes a digital-to-analogue converter, and the filter stages consist of LC (inductive/capacitive) circuits in parallel with each other. If the analogue input becomes too large, the feedback pulses produced by the digital-to-analogue converter will fail to cancel the analogue input, and the residual signal will build up in the filter stages, the signal increasing in each successive filter stage. When the input again falls within acceptable limits, the output of the converter remains controlled almost entirely by the continuing oscillations in the third and fourth stages and cannot revert to being representative of the input signal unless special reset means is provided.
It has been proposed to recover from such a situation by providing reset means which provides a short circuit across the third and fourth stage LC circuits when the output of the third and fourth stages exceeds predetermined values. But this temporarily interrupts operation of the converter, corrupting the output.
The Applicants have also proposed (GB-A-93 071 645) to provide limiters on the outputs of the third and fourth filter stages in an attempt to provide overload recovery. While limiters are sufficient to provide overload recovery for a third order sigma-delta converter (i.e. a circuit with three filter stages), attempts to provide overload recovery for a fourth order sigma-delta converter using the limiters have so far proved unsuccessful.
In deriving the present invention, the Applicants have now considered the problem of overload recovery from a radically different viewpoint. In particular, they have made use of the fact that a second order sigma-delta converter/modulator is inherently stable i.e. recovers from overload.
In FIG. 3, the architecture of FIG. 1 is repeated, except that the filter means 4 has been reduced to two stages, and the feedforward path 5a has been supplemented by an additional feedforward path 5b with a different transfer function. V.sub.e and V.sub.3 represent the change in error voltage following adder 3, and in the second feedforward path, respectively, in response to an input V.sub.2 applied before the quantising means 1. V.sub.e and V.sub.3 are of course additional to voltages representing quantisation noise q and input voltage V.sub.in.
When operating in an oversampled sigma-delta modulator/converter, the quantiser may be modelled as a linear gain amplifier with the addition of quantising noise q.
In FIG. 3, assuming V.sub.in =0, and that the linearised gain of the quantiser is unity.
V.sub.out =V.sub.out .multidot..beta..multidot.A.sub.1 +V.sub.2 +q, where V.sub.out is the output voltage, .beta. the transfer function of the feedback path, and A.sub.1 the transfer function of the filter means 4 in the feedforward path 5a. EQU Thus, V.sub.out (1=.beta..multidot.A.sub.1)=V.sub.2 +q EQU and V.sub.out =V.sub.2 /(1=.beta..multidot.A.sub.1)+q/(1-.beta. A.sub.a) EQU but V.sub.e =.beta.V.sub.out EQU so V.sub.e =V.sub.2 .beta./(1-.beta..multidot.A)+q.beta./(1-.beta. A.sub.1) .
Hence the effect of adding in a voltage V.sub.2 before the quantising means is to add a voltage of V.sub.2 .beta.(1-.beta. A.sub.1) to the error signal. If now this voltage passes through the filter means 4 along a path having a transfer function 1-.beta. A.sub.1, then EQU V.sub.3 =.beta. V.sub.2.
If .beta. is unity gain and just represents a delay, it follows that the path from where V.sub.2 is injected to V.sub.3 acts as a simple delay.
Thus if a further filter is connected between V.sub.3 and V.sub.2, the circuit behaves as if the filter was connected in a loop containing quantising means 1, an input V.sub.in and a delay i.e. a sigma-delta loop. Note that this only applies while the loop containing the filter means 4 in its output along feedforward path 5a is not overloaded.
Thus, the benefits of higher filter order noise shaping can be obtained without the problem of instability by arranging that the highest order of the filter appears to be set in its own sigma-delta circuit. This applies to analogue-to-digital converters for continuous and sampled data signals, as well as to digital modulators.